- Email: [email protected]
A determination of two Michel parameters in purely leptonic tau decays
Physics Letters B 316 (1993) 608-614 North-Holland
PHYSICS LETTERS B
A determination of two Michel parameters in purely leptonic tau decays ARGUS Collaboration H. Albrecht, H. Ehrlichmann, T. Hamacher, R.P. Hofmann, T. Kirchhoff, A. Nau, S. Nowak l, H. Schr6der, H.D. Schulz, M. Walter 1, R. Wurth DESY, Hamburg, Germany
C. Hast, H. Kolanoski, A. Kosche, A. Lange, A. Lindner, R. Mankel, M. Schieber, T. Siegmund, B. Spaan, H. Thurn, D. TSpfer, D. Wegener Institut far Physik2, Universitiit Dortmund, Germany
M. Bittner, P. Eckstein Institut far Kern- und Teilchenphysik 3, Technische Universiti~t Dresden, Germany
M. Paulini, K. Reim, H. Wegener Physikalisches Institut 4, Universitiit Erlangen-Niirnberg, Germany
R. Eckmann, R. Mundt, T. Oest, R. Reiner, W. Schmidt-Parzefall II. Institut far Experimentalphysik, Universitiit Hamburg, Germany
W. Funk, J. Stiewe, S. Werner lnstitut far Hochenergiephysik 5, Universitiit Heidelberg, Germany
K. Ehret, W. Hofmann, A. Hiipper, S. Khan, K.T. Kn6pfle, M. Seeger, J. Spengler Max-Planck-Institut far Kernphysik, Heidelberg, Germany
D.I. Britton 6, C.E.K. Charlesworth 7, K.W. Edwards 8, E.R.F. Hyatt 6, H. Kapitza s, P. Krieger 7, D.B. MacFarlane 6, P.M. Patel 6, J.D. Prentice 7, P.R.B. Saull 6, K. Tzamariudaki 6, R.G. Van de Water 7, T.-S. Yoon 7 Institute of Particle Physics9, Canada
D. ReBing, M. Schmidtler, M. Schneider, K.R. Schubert, K. Strahl, R. Waldi, S. Weseler Institut far Experimentelle Kernphysik l°, UniversiRit Karlsruhe, Germany
G. Kernel, P. Kri~an, E. Kri~ni~, T. Podobnik, T. ~ivko lnstitut J. Stefan and Oddelek za fiziko 11, Univerza v Ljubljani, Ljubljana, Slovenia
608
0370-2693/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 316, number 4
PHYSICS LETTERSB
28 October 1993
V. B a l a g u r a , I. B e l y a e v , S. C h e c h e l n i t s k y , M. D a n i l o v , A. D r o u t s k o y , Y u . G e r s h t e i n , A. G o l u t v i n , G . K o s t i n a , D . L i t v i n t s e v , V. L u b i m o v , P. P a k h l o v , F. R a t n i k o v , S. S e m e n o v , A. S n i z h k o , V. S o l o s h e n k o , I. T i c h o m i r o v a n d Y u . Z a i t s e v
Institute of Theoretical and Experimental Physics, Moscow, Russia Received 20 August 1993 Editor: K. Winter
Using the ARGUS detector at the e+e - storage ring DORIS II, we have determined the Michel parameters p and of z --- ~tu~-and T --- euF decays. From a data sample with 333 events/pb around vt~ = 10 GeV, we select 3230 events e+e - --- r + z - ---, (lz+v~)(e~:u~) and determine p from the e and p momentum spectra and ~ from the correlations between e and/t momenta. For p we obtain P~--.e = 0.79 + 0.08 + 0.06 and p r ~ = 0.76 + 0.07 -t- 0.08 in accordance with the V - A structure of the decays. The momentum correlations are only sensitive to the product ~r~e~T~u. Setting ~T--e = ~ r ~ , we obtain I~d = 0.90 + 0.15 + 0.10 also in accordance with V - A. The updated decay fractions are B(z --. eu~') = (17.5 -4-0.3 ± 0.5)% and B(z ---./tv~') = (17.4 ± 0.3 ± 0.5)%.
M u o n decay has been investigated for determining the space-time structure of the weak interaction for more than 40 years. The m u o n lifetime r , and the four Michel parameters [ 1-3 ] #1 p,, ~/,, ~,, j , have been determined to + 18 ppm, +0.35%, + 1.3%, +0.8%, and 4-0.5%, respectively. The value of r~ fixes one of the 18 parameters of the Standard Model, and the other four obtained values are in perfect agreement with
1 DESY, IfH Zeuthen. 2 Supported by the German Bundesministerium fiir Forschung und Technologic under contract number 054DO51P. 3 Supported by the German Bundesministerium f'tir Forschung und Technologic, under contract number 055DD1 IP. 4 Supported by the German Bundesministerium fiir Forschung und Technologie under contract number 054ERI2P. 5 Supported by the German Bundesministerium fiir Forschung und Technologic under contract number 055HD21P. 6 McGill University, Montreal, Quebec, Canada. 7 University of Toronto, Toronto, Ontario, Canada. s Carleton University, Ottawa, Ontario, Canada. 9 Supported by the Natural Sciences and Engineering Research Council Canada. 10 Supported by the German Bundesministerium f'tir Forschung und Technologic under contract number 054KA 17P. 11 Supported by the Department of Science and Technology of the Republic of Slovenia and the Internationales Biiro KfA, Jiilich. #1 For definitions and further references see e.g. Fetscher and Gerber [4].
standard W-boson exchange, i.e. with a V - A structure predicting 3/4, 0, 1, and 3/4 for the Michel parameters. In spite of the good experimental precisions reached, an overall analysis with all possible weak couplings [4] leaves much room for decay contributions in addition to those from the standard W-boson. The much higher mass of the r-lepton is, therefore, a strong motivation to search for deviations of F ( r ---, l u g ) , p~, r/t, ~ , and J, from their V - A predictions in z e v ~ and r ~ /~u~ decays. Hadronic r decays allow also a direct determination of the z-neutrino helicity h~, and a test of its V - A value h~, = - 1. After the recent improvement on the precision of the r-lepton mass [5-7], the measured rate F ( r --+ eu-ff) agrees with its V - A prediction F(/~ ---, ev-ff)(m~/m,) 5. The results on p, with an experimental mean of 0.727-t- 0.033 [ 8 ] also support V - A, and the first direct observation of parity violation in r decays, h~ = - 1.25 + 0.23 +0.08 -0.15 [9,10], demonstrates that the r-neutrino is indeed left-handed. In this paper, we report on a measurement of the parityviolating Michel parameter ~ from 3230 r + r - ---, (/~±v~)(e~:v-ff) events and on simultaneously obtained results for p~ and F ( r ~ £u~). In the r rest frame, neglecting radiative corrections 2 2 and terms proportional to mt/m~, the energy spectrum of the charged decay lepton ! is given by
609
Volume 316, number 4
PHYSICS LETTERS B
dFr~tt'~" (x x 2
dl2dx x (12(1-x)
+p~(-~x-8)
- P,~,cosO[4(1 - x )
2Et/m~
+rhmtm~2 4 ( 1 x - X )
+ dT(3w2X-- 8 ) ] ~ , /
where x = is the scaled lepton energy, P, the polarisation, and O the angle between the r spin and the lepton momentum. With unpolarised r-leptons, or integrating over the full O range, the spectrum depends only on p~ and r/~. Measurements of the other two Michel parameters require polarised taus. Electronpositron annihilation produces z pairs with simple correlations between the two r spins. At high energies, there are only events with both spins parallel, eit h e r ( P , + = +1, P r = - l ) o r ( P ~ + = - 1 , P, + 1 ). Their probabilities are equal as long as Z ° contributions are negligible. This spin structure correlates the two charged lepton momenta in r + r (e~=t,~) events if both ~,-e and ~ - ~ are nonzero. An observation of e and g momentum correlations gives a measurement of the product ~ _ e ~ . The experiment has been performed in e+e - annihilation at centre-of-mass energies around 10 GeV with the A R G U S detector at the storage ring DORIS II. The storage ring is described in [ 11 ], A R G U S and its performance in [ 12 ]. The data sample used for this analysis has been collected between 1985 and 1989, and its integrated luminosity has been determined to be (333 + 10)/pb. This is not the full data sample of A R G U S as used in most other analyses. Since the analysis of two-prong events requires careful attention of the trigger thresholds, we have restricted the data sample to those run periods where the trigger efficiency was well under control. Events are selected with exactly two tracks of opposite charge. Each track must have a transverse momentum above 80 MeV/c, a polar angle with I cos 01 < 0.7, and must point to the primary interaction region defined by the cuts r < 1.5 cm and Izl < 5 cm. Electron and muon candidates are selected by requiring a muon likelihood L~ > 0.8 and an electron likelihood L~ < 0.1 for muons and Le > 0.8, L , < 0.1 for electrons. In order to keep high efficiency and small misidentification probabilities, we require electrons to have p > 0.65 G e V / c and muons p > 1.30 GeV/c. Events
(g±v-ff)
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28 October 1993
with neutrinos are enriched by the two event cuts cos aacol > - 0 . 9 9 9 7 and mmiss > 2 GeV/c 2, where the acollinearity is defined as cos aacol = P e'P ~/( ~ el"M ,I ) and mmiss is the missing mass in the event obtained f r o m mrnis s 2 = ( X / ~ - Ee - E~) 2 - (Pc + pv)2. There remain 3336 events after these cuts. Electron identification is studied in radiative Bhabha events and converted photons [ 13]. The efficiency of the likelihood cuts as used in this analysis is found to increase from 0.40 at 0.65 GeV/c to 0.90 at 2 GeV/c and is nearly constant above 2 GeV/c. Electron misidentification of muons and pions is obtained from samples of cosmic muons and reconstructed K ° decays in multihadronic events. In the Pe and cos 0 region of the present analysis, pions fake an electron with 0.6% probability and muons fake electrons with a probability rapidly decreasing from 2.0% at 0.6 GeV/c to zero at 1.0 GeV/c. Muon efficiencies are obtained from a Monte Carlo simulation which is cross-checked with cosmic ray measurements. The efficiency rises from 0.45 at 1.3 G e V / c to 0.78 above 2 GeV/c. Misidentification from electrons and pions is obtained from the Bhabha and K ° samples mentioned above. Pions fake muons with a probability of 2.0% and electrons fake a muon with a probability decreasing from 1.5% at 1.3 GeV/c to 0.3% at 5 GeV/c. Very detailed studies are also performed for all levels of the A R G U S trigger as functions of time and particle angle and momentum. Single track efficiencies in the second level trigger vary between 0.75 and 0.92 during the selected run periods. The geometrical acceptance for r + r --* (ev~) (/~v~) events is obtained by the A R G U S detector simulation using KORAL-B [14] for r+T - pair generation with initial state radiation and T A U O L A [ 15 ] for r decays including PHOTOS [ 16 ] for final state radiation. Assuming standard V - A decays, the overall efficiency for ( e v ~ ) ( # v ~ ) events, including geometry, selection, and reconstruction, is found to be (17.3 + 0.1)%. Since T A U O L A contains only combinations of V and A for the decay structure, the generator has been modified for this analysis in order to generate r ~ et, V decays with arbitrary values of p, r/, ~, and ~ [ 17 ]. Monte Carlo simulations are also used to estimate the non (ev~) ( g v ~ ) background in the selected event sample, table 1 summarizes the results. The total background amounts to 106, leaving 3230 signal events.
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PHYSICS LETTERSB
Table 1 Estimated number of background events in the selected sample of 3336 (ev~) (/zv~) events. The notation 7tv includes the decay modes nv and pv. The errors include misidentification uncertainties and are therefore correlated. e+e e+e r+r r+r z+z z+r z+r -
--, e+e - (7) and p + g - (2)) --, e + e - p + p - (y) --~ (ev~-)(ev~) ~ (pv'ff)(pv'ff) ~ (nv)(ev~) -* (nv)(pv'ff) ---, ( n v ) ( n v )
. . . .
i
....
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i ....
i ....
tin
(a)
10 4- 27 13 + 5 164- 5 6+ 2 45 -4- 10 15+ 3 < 1
From the n u m b e r of selected events, the energyweighted integrated luminosity, the overall event acceptance, and the backgrounds in table 1, we obtain the product of decay fractions, B ( z ---, e v ~ ) B ( z ---, /~t,~) = 0.03134-0.00064-0.0016, where the first error is statistical and the second systematic. The systematic error is the quadratic sum of 3% from luminosity, 4% from m u o n acceptance and identification, 1% from electron identification, and less than 1% from geometry, trigger, reconstruction, and background. The result is in good agreement with our previous result [ 18 ] and with the world average [ 8 ]. The data samples used in the previous analysis [18] of r+z :F ~ ( e + v ~ ) ( / ~ : v ~ - ) events and in the present analysis overlap partiallly. The combined result of both analyses is B ( z ~ e v ~ ) B ( z --. g v ~ ) = 0.0306 4- 0.0005 5:0.0013 ; it replaces our earlier value [18]. Using the measured ratio of m u o n s to electrons in ref. [ 18 ], B (r p v - f f ) / B ( z ~ et,~) = 0.9974-0.0354-0.040, together with our combined result for the product, we obtain B ( r ~ ev~) = (17.5 + 0.3 4- 0.5)%, B(r--* p u ~ ' ) =
28 October 1993
(17.44-0.3+0.5)%.
Using recent z mass [6] and lifetime [8] values, this leads to z f f B ( z ~ ev~') = (1.067 4- 0.041 ) z u ( m u / m ~ ) 5, which fulfills the lepton universality of the Standard Model within 1.6 standard deviations.
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Fig. 1. Observed momentum spectra ofmuons (a) and electrons (b) after background subtraction, without acceptance correction, in arbitrary units. The solid curves are the best fit results with free parameters Pz--e, r/z--,e and Pr--,p, r/,_..p, respectively. The dashed curves, in order to demonstrate the sensitivities on p, are drawn with p = r/ = 0. The Michel parameters p~--.u and p~-e are obtained from the m u o n and electron m o m e n t u m spectra, shown in fig. 1. In contrast to earlier analyses, P ~ u is not obtained from a fit with fixed ~/~_.u = 0; instead both p and t/are allowed to vary within their physical boundaries. This variation does not require a large n u m b e r of Monte Carlo generations. Because of the linear dependence on p and r/, only three sets are required, and the most general form of the m o m e n t u m spectrum is given by 611
Volume 316, number 4
PHYSICS LETTERS B
28 October 1993
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The result o f a X 2 fit to the muon spectrum in fig. l a is shown in fig. 2. The sensitivity on r/ is very weak because its contribution to the spectrum is weighted with mu/mr. The X 2 value at the m i n i m u m is 72.3 for 74 degrees o f freedom. F o r fixed r/r_u = 0, we obtain p~_~ = 0.76+0.06. Taking the weak correlation with ~/~_~ into account, we obtain
i
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p Fig. 2. The dotted polygon shows the allowed range for p and ~/with arbitrary V, A, S, P, and T couplings. The solid point is the best fit for (p, r/) from the muon m o m e n t u m spectrum, and the two nearly parallel bands are the one and two sigma contours around this point. The bands show that any r/ value in the allowed range is compatible with our data set. Because o f the weak p-~/ correlation, our quoted error on p with free r/ is slightly larger than the error on p with r/ = 0 as shown by the open point.
. . . .
5.0
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Fig. 3. Electron vs. muon momentum in the 3336 selected (#v~) (ev~) events. allowed range is within the one sigma contour. A X 2 fit to the electron spectrum gives p e t e = 0.79 + 0.08 ± 0.06. The correlation with r/T--,e is negligible because o f m¢/mT. The systematic error is d o m i n a t e d by the background subtraction. The two p results agree well with our earlier value [19]. This was obtained from r+r + ---, (~+vV)(~r+rr+rr-v) events; i.e. our old and new values are statistically independent. The p~ vs. p~ biplot as shown in fig. 3 exhibits a slight preference for low-low and high-high momentum pairs, demonstrated by the correlation coefficient which is found to be k =
~(P°-~)
(p~ - ~ )
~/E (po_~)2 Z]fp. _~)2
= +0.065 ± 0.020. p,._,u = 0.76 + 0.07 + 0.08, where the systematic error has its d o m i n a n t contributions from background subtraction (+0.07) and from the m o m e n t u m dependence o f the muon identification (±0.03). As seen in fig. 2, the fit to the muon spectrum does not constrain r/~_~; any value in the 612
The positive correlation is in fact generated by initial state radiation and by the product ~ r - e ~ - u . The Monte Carlo simulation gives k = + 0.018 for zero values and k = +0.055 for the V - A values ~ _ ~ = ~ _ u = 1. Being sensitive to the product, the experimental value of k proves that ~ - e and ~,-.u have
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220.0
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28 October 1993
,
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x,,~,= 202.2 at I(I = 0.90 200.0 -1.0
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Fig. 4. Dependence of X2 on ~ = ~r--¢ = ~r--u as result of a fit to the three-dimensional Pe, Pu, a aeol distribution. the same sign and are both either close to + 1 or close to - 1. More information is obtained from a twodimensional fit to the pe vs. Pu distribution. Because o f a slight additional increase in information, we actually perform a Z 2 fit in three dimensions with ten bins o f pc, ten bins ofpu, and two bins o f aacol, above and below cos a = - 0 . 9 2 . The bin widths have been chosen on the basis o f equal bin contents. The fit is only sensitive to the product o f both I values, we therefore use electron-muon universality I~ = l ~ - c = I , ~ u . Since (p, r/) and (~, ~) are uncorrelated, we perform the ~ fits with fixed values p = 3/4 and ~/ = 0. The X2 distribution o f the I fit with fixed value = 3/4 is shown in fig. 4. It is obtained by comparing the numbers o f events in 200 bins with the expectations from a total o f 72 000 Monte Carlo events. There is again a technique which avoids the generation o f separate Monte Carlo sets for each value o f I. The program KORAL-B [ 14 ] works with I - d e p e n d e n t weights which are used for event selection on a hitor-miss basis. In the analysis here, each Monte Carlo event surviving the p and q hit-or-miss is retained, and its weights for 100 values o f ~ are stored for the X 2 tests which compare the distributions of the data and the weighted Monte Carlo events. The X 2 distribution is symmetric a r o u n d l = 0 and has its minima at Ill = 0.90. The X2minvalue of 202.2 matches well with the 198 degrees of freedom. The difference ~ 2 ( ~ = 0 ) -- )~2in i s 14.9, i.e. our event distribution
excludes parity conservation with 3.9 standard deviations. With one standard deviation we obtain I l l = 0.90 + 0.13, which agrees well with the V - A prediction I = 1. A two-dimensional fit to only Pe and Pu gives Ill = 0.95 + 0.20. Fits o f Monte Carlo to Monte Carlo distributions prove that our applied method is bias-free. Increasing the low-momentum cuts to 0.8 and 1.5 G e V / c for e a n d / l , respectively, changes I only in the statistically expected range. The systematic error has contributions from background, m o m e n t u m dependence o f the muon efficiency, and initial and final state radiation. Final state radiation is negligible, background subtraction gives z~ --- +0.08, muon efficiency ±0.02, and initial state radiation 4-0.06. The latter contribution may be overestimated; it is obtained by changing the electric coupling constant a in KORAL-B to 1.01a. Adding the contributions quadratically, our result is
II~l
= 0.90+0.13-4-0.10,
where the parameter 63 is fixed at its V - A value 6, = 3/4. Varying 6, in its allowed range, the statistical error is estimated to increase to +0.15. Our final result with free ~, is [I~[ = 0 . 9 0 + 0 . 1 5 + 0 . 1 0 . 613
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The m o m e n t u m - m o m e n t u m correlation for determining ~ is a scalar observable and can, therefore, not be parity-violating. This is reflected by the fact that our observation is in as good agreement with (V + A ) ( V + A), ~r = - 1 , as with (V - A ) ( V - A), ~ = + 1. However, the source for ~ # 0 must be parity violation; the electron (or m u o n ) m o m e n t u m is correlated with the tau spin, and this pseudoscalar is non-zero. Measurements at LEP determine the sign o f ~ . Following a recent analysis of Privitera [20], the mean values of the four LEP experiments [21-24] for ~PT and h~,P~ are - 0 . 0 8 9 + 0.054 and 0.143 + 0.028, respectively, where P, is the tau polarisation in Z ° ~ r + z - , ~r is the mean Michel parameter in r ~ evV" and r ~ pv~-decays, and h~, the mean observed z-neutrino helicity in r ---, ztu, r --. pu, and z ~ al~,. Combining this with the A R G U S measurement h~, = - 1.25 + 0.23 +0.0s -0.15 [10] gives the model-independent result ~ ( L E P ) = + 0 . 7 8 + 0.52 which is 3.4 standard deviations from --1.
To conclude, we have determined updated values for the purely leptonic decay fractions o f the tau lepton, B(z ~ e v ~ ) = (17.5 + 0.3 ± 0.5)%, B(z /~v~) = ( 17.4 + 0.3 ± 0.5)%, which replace our earlier results in ref. [ 18 ]. The new values are in agreement with the Standard Model expectation. Using recent r mass [6] and lifetime [8] values, we obtain rr/B(r ~ evV') = ( 1 . 0 6 7 4 - 0 . 0 4 1 ) z g ( m g / m r ) 5. Our Michel parameter results P , - e = 0.79 4- 0.08 ± 0.06 and p , _ u = 0.76 ± 0.07 4- 0.08 are statistically independent from our earlier one in ref. [19] and agree well with the Standard Model value p = 3/4. The asymmetry parameter is found to be I~1 = 0.90 ± o. 15 ± o. 10 in also good agreement with the Standard Model value ~ = 1. Note added after completion. The analysis has been performed with the KORAL-B version of 1992. We have carefully controlled, not by repeating the full analysis but by comparing different Monte Carlo samples on the generator level, that the new KORAL-B version o f May 1993 leads to only negligible shifts in the fit result for ~ . The values of B ( r ~ gv~) and pr are not affected by the change in KORAL-B. We thank U. Djuanda, E. Michel, and W. Reinsch for their competent technical help in running the
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experiment and processing the data. We also thank H. Nesemann, B. Sarau, and the D O R I S group for operating the storage ring. We gratefully acknowledge discussions on tau decays with J.H. Kiihn, Z. W~ls, and W. Fetscher. The visiting groups wish to thank the DESY directorate for hospitality and support.
References [1] L. Michel, Proc. Phys. Soc. London A 63 (1950) 514. [2] C. Bouchiat and L. Michel, Phys. Rev. 106 (1957) 170. [3] L. Okun and A. Rudik, J. Expt. Theor. Phys. (USSR) 32 (1957) 627 [Sov. Phys. JETP 6 (1957) 520]. [4] W. Fetscher, H.J. Gerber and K.F. Johnson, Phys. Lett. B 173 (1986) 102. [5] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 292 (1992) 221. [6] BES Collab., J.Z. Bai et al., Phys. Rev. Lett. 69 (1992) 3021. [7] CLEO Collab., R. Ballest et al., A Measurement of the Tau Lepton Mass, Cornell preprint CLNS 93/1194 (1993), submitted to Phys. Rev. D. [8] Particle Data Group, K. Hikasa et al., Review of Particle Properties, Phys. Rev. D 45 (1992) Part II. [9] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 250 (1990) 164. [10] ARGUS CoUab., H. Albrecht et al., Z. Phys. C 58 (1993) 61. [ 11 ] K. Wille, DESY 81-047 ( 1981 ). [ 12 ] ARGUS CoUab., H. Albrecht et al., Nucl. Instr. Meth. A 275 (1989) 1. [ 13] Efficiency determinations and more details of the measurement can be found in K. Strahl, Dr. rer. nat. Thesis, Universittit Kadsruhe (1992), Karlsruhe preprint IEKP-KA/92-14. [14] S. Jadach and Z. W~ts, CERN-TH-5855/90 (1990). [ 15 ] S. Jadach, J.H. Kiihn and Z. Wos, CERN-TH-5856/90 (1990). [16] E. Barberio, B. van Eijk and Z. W~Is, CERN-TH5857/90 (1990). [ 17 ] M. Schmidtler (ARGUS), unpublished. [18]ARGUS Collab., H. Albrecht et al., Z. Phys. C 53 (1992) 367. [ 19 ] ARGUS CoUab., H. Albrecht et al., Phys. Lett. B 246 (1990) 278. [20] P. Privitera, Phys. Lett. B 288 (1992) 227. [211 ALEPH CoUab., D. Decamp et al., Phys. Lett. B 265 (1991) 430. [22] OPAL Collab., G. Alexander et al., Phys. Lett. B 266 (1991) 201. [23 ] DELPHI CoUab., P. Abreu et al., Z. Phys. C 55 (1992) 555. [24] L3 Collab., O. Adriani et al., Phys. Lett. B 294 (1992) 466.
PHYSICS LETTERS B
A determination of two Michel parameters in purely leptonic tau decays ARGUS Collaboration H. Albrecht, H. Ehrlichmann, T. Hamacher, R.P. Hofmann, T. Kirchhoff, A. Nau, S. Nowak l, H. Schr6der, H.D. Schulz, M. Walter 1, R. Wurth DESY, Hamburg, Germany
C. Hast, H. Kolanoski, A. Kosche, A. Lange, A. Lindner, R. Mankel, M. Schieber, T. Siegmund, B. Spaan, H. Thurn, D. TSpfer, D. Wegener Institut far Physik2, Universitiit Dortmund, Germany
M. Bittner, P. Eckstein Institut far Kern- und Teilchenphysik 3, Technische Universiti~t Dresden, Germany
M. Paulini, K. Reim, H. Wegener Physikalisches Institut 4, Universitiit Erlangen-Niirnberg, Germany
R. Eckmann, R. Mundt, T. Oest, R. Reiner, W. Schmidt-Parzefall II. Institut far Experimentalphysik, Universitiit Hamburg, Germany
W. Funk, J. Stiewe, S. Werner lnstitut far Hochenergiephysik 5, Universitiit Heidelberg, Germany
K. Ehret, W. Hofmann, A. Hiipper, S. Khan, K.T. Kn6pfle, M. Seeger, J. Spengler Max-Planck-Institut far Kernphysik, Heidelberg, Germany
D.I. Britton 6, C.E.K. Charlesworth 7, K.W. Edwards 8, E.R.F. Hyatt 6, H. Kapitza s, P. Krieger 7, D.B. MacFarlane 6, P.M. Patel 6, J.D. Prentice 7, P.R.B. Saull 6, K. Tzamariudaki 6, R.G. Van de Water 7, T.-S. Yoon 7 Institute of Particle Physics9, Canada
D. ReBing, M. Schmidtler, M. Schneider, K.R. Schubert, K. Strahl, R. Waldi, S. Weseler Institut far Experimentelle Kernphysik l°, UniversiRit Karlsruhe, Germany
G. Kernel, P. Kri~an, E. Kri~ni~, T. Podobnik, T. ~ivko lnstitut J. Stefan and Oddelek za fiziko 11, Univerza v Ljubljani, Ljubljana, Slovenia
608
0370-2693/93/$ 06.00 © 1993 Elsevier Science Publishers B.V. All rights reserved.
Volume 316, number 4
PHYSICS LETTERSB
28 October 1993
V. B a l a g u r a , I. B e l y a e v , S. C h e c h e l n i t s k y , M. D a n i l o v , A. D r o u t s k o y , Y u . G e r s h t e i n , A. G o l u t v i n , G . K o s t i n a , D . L i t v i n t s e v , V. L u b i m o v , P. P a k h l o v , F. R a t n i k o v , S. S e m e n o v , A. S n i z h k o , V. S o l o s h e n k o , I. T i c h o m i r o v a n d Y u . Z a i t s e v
Institute of Theoretical and Experimental Physics, Moscow, Russia Received 20 August 1993 Editor: K. Winter
Using the ARGUS detector at the e+e - storage ring DORIS II, we have determined the Michel parameters p and of z --- ~tu~-and T --- euF decays. From a data sample with 333 events/pb around vt~ = 10 GeV, we select 3230 events e+e - --- r + z - ---, (lz+v~)(e~:u~) and determine p from the e and p momentum spectra and ~ from the correlations between e and/t momenta. For p we obtain P~--.e = 0.79 + 0.08 + 0.06 and p r ~ = 0.76 + 0.07 -t- 0.08 in accordance with the V - A structure of the decays. The momentum correlations are only sensitive to the product ~r~e~T~u. Setting ~T--e = ~ r ~ , we obtain I~d = 0.90 + 0.15 + 0.10 also in accordance with V - A. The updated decay fractions are B(z --. eu~') = (17.5 -4-0.3 ± 0.5)% and B(z ---./tv~') = (17.4 ± 0.3 ± 0.5)%.
M u o n decay has been investigated for determining the space-time structure of the weak interaction for more than 40 years. The m u o n lifetime r , and the four Michel parameters [ 1-3 ] #1 p,, ~/,, ~,, j , have been determined to + 18 ppm, +0.35%, + 1.3%, +0.8%, and 4-0.5%, respectively. The value of r~ fixes one of the 18 parameters of the Standard Model, and the other four obtained values are in perfect agreement with
1 DESY, IfH Zeuthen. 2 Supported by the German Bundesministerium fiir Forschung und Technologic under contract number 054DO51P. 3 Supported by the German Bundesministerium f'tir Forschung und Technologic, under contract number 055DD1 IP. 4 Supported by the German Bundesministerium fiir Forschung und Technologie under contract number 054ERI2P. 5 Supported by the German Bundesministerium fiir Forschung und Technologic under contract number 055HD21P. 6 McGill University, Montreal, Quebec, Canada. 7 University of Toronto, Toronto, Ontario, Canada. s Carleton University, Ottawa, Ontario, Canada. 9 Supported by the Natural Sciences and Engineering Research Council Canada. 10 Supported by the German Bundesministerium f'tir Forschung und Technologic under contract number 054KA 17P. 11 Supported by the Department of Science and Technology of the Republic of Slovenia and the Internationales Biiro KfA, Jiilich. #1 For definitions and further references see e.g. Fetscher and Gerber [4].
standard W-boson exchange, i.e. with a V - A structure predicting 3/4, 0, 1, and 3/4 for the Michel parameters. In spite of the good experimental precisions reached, an overall analysis with all possible weak couplings [4] leaves much room for decay contributions in addition to those from the standard W-boson. The much higher mass of the r-lepton is, therefore, a strong motivation to search for deviations of F ( r ---, l u g ) , p~, r/t, ~ , and J, from their V - A predictions in z e v ~ and r ~ /~u~ decays. Hadronic r decays allow also a direct determination of the z-neutrino helicity h~, and a test of its V - A value h~, = - 1. After the recent improvement on the precision of the r-lepton mass [5-7], the measured rate F ( r --+ eu-ff) agrees with its V - A prediction F(/~ ---, ev-ff)(m~/m,) 5. The results on p, with an experimental mean of 0.727-t- 0.033 [ 8 ] also support V - A, and the first direct observation of parity violation in r decays, h~ = - 1.25 + 0.23 +0.08 -0.15 [9,10], demonstrates that the r-neutrino is indeed left-handed. In this paper, we report on a measurement of the parityviolating Michel parameter ~ from 3230 r + r - ---, (/~±v~)(e~:v-ff) events and on simultaneously obtained results for p~ and F ( r ~ £u~). In the r rest frame, neglecting radiative corrections 2 2 and terms proportional to mt/m~, the energy spectrum of the charged decay lepton ! is given by
609
Volume 316, number 4
PHYSICS LETTERS B
dFr~tt'~" (x x 2
dl2dx x (12(1-x)
+p~(-~x-8)
- P,~,cosO[4(1 - x )
2Et/m~
+rhmtm~2 4 ( 1 x - X )
+ dT(3w2X-- 8 ) ] ~ , /
where x = is the scaled lepton energy, P, the polarisation, and O the angle between the r spin and the lepton momentum. With unpolarised r-leptons, or integrating over the full O range, the spectrum depends only on p~ and r/~. Measurements of the other two Michel parameters require polarised taus. Electronpositron annihilation produces z pairs with simple correlations between the two r spins. At high energies, there are only events with both spins parallel, eit h e r ( P , + = +1, P r = - l ) o r ( P ~ + = - 1 , P, + 1 ). Their probabilities are equal as long as Z ° contributions are negligible. This spin structure correlates the two charged lepton momenta in r + r (e~=t,~) events if both ~,-e and ~ - ~ are nonzero. An observation of e and g momentum correlations gives a measurement of the product ~ _ e ~ . The experiment has been performed in e+e - annihilation at centre-of-mass energies around 10 GeV with the A R G U S detector at the storage ring DORIS II. The storage ring is described in [ 11 ], A R G U S and its performance in [ 12 ]. The data sample used for this analysis has been collected between 1985 and 1989, and its integrated luminosity has been determined to be (333 + 10)/pb. This is not the full data sample of A R G U S as used in most other analyses. Since the analysis of two-prong events requires careful attention of the trigger thresholds, we have restricted the data sample to those run periods where the trigger efficiency was well under control. Events are selected with exactly two tracks of opposite charge. Each track must have a transverse momentum above 80 MeV/c, a polar angle with I cos 01 < 0.7, and must point to the primary interaction region defined by the cuts r < 1.5 cm and Izl < 5 cm. Electron and muon candidates are selected by requiring a muon likelihood L~ > 0.8 and an electron likelihood L~ < 0.1 for muons and Le > 0.8, L , < 0.1 for electrons. In order to keep high efficiency and small misidentification probabilities, we require electrons to have p > 0.65 G e V / c and muons p > 1.30 GeV/c. Events
(g±v-ff)
610
28 October 1993
with neutrinos are enriched by the two event cuts cos aacol > - 0 . 9 9 9 7 and mmiss > 2 GeV/c 2, where the acollinearity is defined as cos aacol = P e'P ~/( ~ el"M ,I ) and mmiss is the missing mass in the event obtained f r o m mrnis s 2 = ( X / ~ - Ee - E~) 2 - (Pc + pv)2. There remain 3336 events after these cuts. Electron identification is studied in radiative Bhabha events and converted photons [ 13]. The efficiency of the likelihood cuts as used in this analysis is found to increase from 0.40 at 0.65 GeV/c to 0.90 at 2 GeV/c and is nearly constant above 2 GeV/c. Electron misidentification of muons and pions is obtained from samples of cosmic muons and reconstructed K ° decays in multihadronic events. In the Pe and cos 0 region of the present analysis, pions fake an electron with 0.6% probability and muons fake electrons with a probability rapidly decreasing from 2.0% at 0.6 GeV/c to zero at 1.0 GeV/c. Muon efficiencies are obtained from a Monte Carlo simulation which is cross-checked with cosmic ray measurements. The efficiency rises from 0.45 at 1.3 G e V / c to 0.78 above 2 GeV/c. Misidentification from electrons and pions is obtained from the Bhabha and K ° samples mentioned above. Pions fake muons with a probability of 2.0% and electrons fake a muon with a probability decreasing from 1.5% at 1.3 GeV/c to 0.3% at 5 GeV/c. Very detailed studies are also performed for all levels of the A R G U S trigger as functions of time and particle angle and momentum. Single track efficiencies in the second level trigger vary between 0.75 and 0.92 during the selected run periods. The geometrical acceptance for r + r --* (ev~) (/~v~) events is obtained by the A R G U S detector simulation using KORAL-B [14] for r+T - pair generation with initial state radiation and T A U O L A [ 15 ] for r decays including PHOTOS [ 16 ] for final state radiation. Assuming standard V - A decays, the overall efficiency for ( e v ~ ) ( # v ~ ) events, including geometry, selection, and reconstruction, is found to be (17.3 + 0.1)%. Since T A U O L A contains only combinations of V and A for the decay structure, the generator has been modified for this analysis in order to generate r ~ et, V decays with arbitrary values of p, r/, ~, and ~ [ 17 ]. Monte Carlo simulations are also used to estimate the non (ev~) ( g v ~ ) background in the selected event sample, table 1 summarizes the results. The total background amounts to 106, leaving 3230 signal events.
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PHYSICS LETTERSB
Table 1 Estimated number of background events in the selected sample of 3336 (ev~) (/zv~) events. The notation 7tv includes the decay modes nv and pv. The errors include misidentification uncertainties and are therefore correlated. e+e e+e r+r r+r z+z z+r z+r -
--, e+e - (7) and p + g - (2)) --, e + e - p + p - (y) --~ (ev~-)(ev~) ~ (pv'ff)(pv'ff) ~ (nv)(ev~) -* (nv)(pv'ff) ---, ( n v ) ( n v )
. . . .
i
....
i . . . .
i ....
i ....
tin
(a)
10 4- 27 13 + 5 164- 5 6+ 2 45 -4- 10 15+ 3 < 1
From the n u m b e r of selected events, the energyweighted integrated luminosity, the overall event acceptance, and the backgrounds in table 1, we obtain the product of decay fractions, B ( z ---, e v ~ ) B ( z ---, /~t,~) = 0.03134-0.00064-0.0016, where the first error is statistical and the second systematic. The systematic error is the quadratic sum of 3% from luminosity, 4% from m u o n acceptance and identification, 1% from electron identification, and less than 1% from geometry, trigger, reconstruction, and background. The result is in good agreement with our previous result [ 18 ] and with the world average [ 8 ]. The data samples used in the previous analysis [18] of r+z :F ~ ( e + v ~ ) ( / ~ : v ~ - ) events and in the present analysis overlap partiallly. The combined result of both analyses is B ( z ~ e v ~ ) B ( z --. g v ~ ) = 0.0306 4- 0.0005 5:0.0013 ; it replaces our earlier value [18]. Using the measured ratio of m u o n s to electrons in ref. [ 18 ], B (r p v - f f ) / B ( z ~ et,~) = 0.9974-0.0354-0.040, together with our combined result for the product, we obtain B ( r ~ ev~) = (17.5 + 0.3 4- 0.5)%, B(r--* p u ~ ' ) =
28 October 1993
(17.44-0.3+0.5)%.
Using recent z mass [6] and lifetime [8] values, this leads to z f f B ( z ~ ev~') = (1.067 4- 0.041 ) z u ( m u / m ~ ) 5, which fulfills the lepton universality of the Standard Model within 1.6 standard deviations.
0.0
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Fig. 1. Observed momentum spectra ofmuons (a) and electrons (b) after background subtraction, without acceptance correction, in arbitrary units. The solid curves are the best fit results with free parameters Pz--e, r/z--,e and Pr--,p, r/,_..p, respectively. The dashed curves, in order to demonstrate the sensitivities on p, are drawn with p = r/ = 0. The Michel parameters p~--.u and p~-e are obtained from the m u o n and electron m o m e n t u m spectra, shown in fig. 1. In contrast to earlier analyses, P ~ u is not obtained from a fit with fixed ~/~_.u = 0; instead both p and t/are allowed to vary within their physical boundaries. This variation does not require a large n u m b e r of Monte Carlo generations. Because of the linear dependence on p and r/, only three sets are required, and the most general form of the m o m e n t u m spectrum is given by 611
Volume 316, number 4
PHYSICS LETTERS B
28 October 1993
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The result o f a X 2 fit to the muon spectrum in fig. l a is shown in fig. 2. The sensitivity on r/ is very weak because its contribution to the spectrum is weighted with mu/mr. The X 2 value at the m i n i m u m is 72.3 for 74 degrees o f freedom. F o r fixed r/r_u = 0, we obtain p~_~ = 0.76+0.06. Taking the weak correlation with ~/~_~ into account, we obtain
i
. . . .
4.0
p(e)
1.0
p Fig. 2. The dotted polygon shows the allowed range for p and ~/with arbitrary V, A, S, P, and T couplings. The solid point is the best fit for (p, r/) from the muon m o m e n t u m spectrum, and the two nearly parallel bands are the one and two sigma contours around this point. The bands show that any r/ value in the allowed range is compatible with our data set. Because o f the weak p-~/ correlation, our quoted error on p with free r/ is slightly larger than the error on p with r/ = 0 as shown by the open point.
. . . .
5.0
[GeV/c]
Fig. 3. Electron vs. muon momentum in the 3336 selected (#v~) (ev~) events. allowed range is within the one sigma contour. A X 2 fit to the electron spectrum gives p e t e = 0.79 + 0.08 ± 0.06. The correlation with r/T--,e is negligible because o f m¢/mT. The systematic error is d o m i n a t e d by the background subtraction. The two p results agree well with our earlier value [19]. This was obtained from r+r + ---, (~+vV)(~r+rr+rr-v) events; i.e. our old and new values are statistically independent. The p~ vs. p~ biplot as shown in fig. 3 exhibits a slight preference for low-low and high-high momentum pairs, demonstrated by the correlation coefficient which is found to be k =
~(P°-~)
(p~ - ~ )
~/E (po_~)2 Z]fp. _~)2
= +0.065 ± 0.020. p,._,u = 0.76 + 0.07 + 0.08, where the systematic error has its d o m i n a n t contributions from background subtraction (+0.07) and from the m o m e n t u m dependence o f the muon identification (±0.03). As seen in fig. 2, the fit to the muon spectrum does not constrain r/~_~; any value in the 612
The positive correlation is in fact generated by initial state radiation and by the product ~ r - e ~ - u . The Monte Carlo simulation gives k = + 0.018 for zero values and k = +0.055 for the V - A values ~ _ ~ = ~ _ u = 1. Being sensitive to the product, the experimental value of k proves that ~ - e and ~,-.u have
Volume 316, number 4
PHYSICS LETTERS B
220.0
,
3,2
,
x 2. . . .
28 October 1993
,
= 217.1 a t I~1 -- 0.0
216.0
212.0
208.0
204.0
x,,~,= 202.2 at I(I = 0.90 200.0 -1.0
i -0.5
i 0.0
, 0.5
1.0
Fig. 4. Dependence of X2 on ~ = ~r--¢ = ~r--u as result of a fit to the three-dimensional Pe, Pu, a aeol distribution. the same sign and are both either close to + 1 or close to - 1. More information is obtained from a twodimensional fit to the pe vs. Pu distribution. Because o f a slight additional increase in information, we actually perform a Z 2 fit in three dimensions with ten bins o f pc, ten bins ofpu, and two bins o f aacol, above and below cos a = - 0 . 9 2 . The bin widths have been chosen on the basis o f equal bin contents. The fit is only sensitive to the product o f both I values, we therefore use electron-muon universality I~ = l ~ - c = I , ~ u . Since (p, r/) and (~, ~) are uncorrelated, we perform the ~ fits with fixed values p = 3/4 and ~/ = 0. The X2 distribution o f the I fit with fixed value = 3/4 is shown in fig. 4. It is obtained by comparing the numbers o f events in 200 bins with the expectations from a total o f 72 000 Monte Carlo events. There is again a technique which avoids the generation o f separate Monte Carlo sets for each value o f I. The program KORAL-B [ 14 ] works with I - d e p e n d e n t weights which are used for event selection on a hitor-miss basis. In the analysis here, each Monte Carlo event surviving the p and q hit-or-miss is retained, and its weights for 100 values o f ~ are stored for the X 2 tests which compare the distributions of the data and the weighted Monte Carlo events. The X 2 distribution is symmetric a r o u n d l = 0 and has its minima at Ill = 0.90. The X2minvalue of 202.2 matches well with the 198 degrees of freedom. The difference ~ 2 ( ~ = 0 ) -- )~2in i s 14.9, i.e. our event distribution
excludes parity conservation with 3.9 standard deviations. With one standard deviation we obtain I l l = 0.90 + 0.13, which agrees well with the V - A prediction I = 1. A two-dimensional fit to only Pe and Pu gives Ill = 0.95 + 0.20. Fits o f Monte Carlo to Monte Carlo distributions prove that our applied method is bias-free. Increasing the low-momentum cuts to 0.8 and 1.5 G e V / c for e a n d / l , respectively, changes I only in the statistically expected range. The systematic error has contributions from background, m o m e n t u m dependence o f the muon efficiency, and initial and final state radiation. Final state radiation is negligible, background subtraction gives z~ --- +0.08, muon efficiency ±0.02, and initial state radiation 4-0.06. The latter contribution may be overestimated; it is obtained by changing the electric coupling constant a in KORAL-B to 1.01a. Adding the contributions quadratically, our result is
II~l
= 0.90+0.13-4-0.10,
where the parameter 63 is fixed at its V - A value 6, = 3/4. Varying 6, in its allowed range, the statistical error is estimated to increase to +0.15. Our final result with free ~, is [I~[ = 0 . 9 0 + 0 . 1 5 + 0 . 1 0 . 613
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PHYSICS LETTERS B
The m o m e n t u m - m o m e n t u m correlation for determining ~ is a scalar observable and can, therefore, not be parity-violating. This is reflected by the fact that our observation is in as good agreement with (V + A ) ( V + A), ~r = - 1 , as with (V - A ) ( V - A), ~ = + 1. However, the source for ~ # 0 must be parity violation; the electron (or m u o n ) m o m e n t u m is correlated with the tau spin, and this pseudoscalar is non-zero. Measurements at LEP determine the sign o f ~ . Following a recent analysis of Privitera [20], the mean values of the four LEP experiments [21-24] for ~PT and h~,P~ are - 0 . 0 8 9 + 0.054 and 0.143 + 0.028, respectively, where P, is the tau polarisation in Z ° ~ r + z - , ~r is the mean Michel parameter in r ~ evV" and r ~ pv~-decays, and h~, the mean observed z-neutrino helicity in r ---, ztu, r --. pu, and z ~ al~,. Combining this with the A R G U S measurement h~, = - 1.25 + 0.23 +0.0s -0.15 [10] gives the model-independent result ~ ( L E P ) = + 0 . 7 8 + 0.52 which is 3.4 standard deviations from --1.
To conclude, we have determined updated values for the purely leptonic decay fractions o f the tau lepton, B(z ~ e v ~ ) = (17.5 + 0.3 ± 0.5)%, B(z /~v~) = ( 17.4 + 0.3 ± 0.5)%, which replace our earlier results in ref. [ 18 ]. The new values are in agreement with the Standard Model expectation. Using recent r mass [6] and lifetime [8] values, we obtain rr/B(r ~ evV') = ( 1 . 0 6 7 4 - 0 . 0 4 1 ) z g ( m g / m r ) 5. Our Michel parameter results P , - e = 0.79 4- 0.08 ± 0.06 and p , _ u = 0.76 ± 0.07 4- 0.08 are statistically independent from our earlier one in ref. [19] and agree well with the Standard Model value p = 3/4. The asymmetry parameter is found to be I~1 = 0.90 ± o. 15 ± o. 10 in also good agreement with the Standard Model value ~ = 1. Note added after completion. The analysis has been performed with the KORAL-B version of 1992. We have carefully controlled, not by repeating the full analysis but by comparing different Monte Carlo samples on the generator level, that the new KORAL-B version o f May 1993 leads to only negligible shifts in the fit result for ~ . The values of B ( r ~ gv~) and pr are not affected by the change in KORAL-B. We thank U. Djuanda, E. Michel, and W. Reinsch for their competent technical help in running the
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experiment and processing the data. We also thank H. Nesemann, B. Sarau, and the D O R I S group for operating the storage ring. We gratefully acknowledge discussions on tau decays with J.H. Kiihn, Z. W~ls, and W. Fetscher. The visiting groups wish to thank the DESY directorate for hospitality and support.
References [1] L. Michel, Proc. Phys. Soc. London A 63 (1950) 514. [2] C. Bouchiat and L. Michel, Phys. Rev. 106 (1957) 170. [3] L. Okun and A. Rudik, J. Expt. Theor. Phys. (USSR) 32 (1957) 627 [Sov. Phys. JETP 6 (1957) 520]. [4] W. Fetscher, H.J. Gerber and K.F. Johnson, Phys. Lett. B 173 (1986) 102. [5] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 292 (1992) 221. [6] BES Collab., J.Z. Bai et al., Phys. Rev. Lett. 69 (1992) 3021. [7] CLEO Collab., R. Ballest et al., A Measurement of the Tau Lepton Mass, Cornell preprint CLNS 93/1194 (1993), submitted to Phys. Rev. D. [8] Particle Data Group, K. Hikasa et al., Review of Particle Properties, Phys. Rev. D 45 (1992) Part II. [9] ARGUS Collab., H. Albrecht et al., Phys. Lett. B 250 (1990) 164. [10] ARGUS CoUab., H. Albrecht et al., Z. Phys. C 58 (1993) 61. [ 11 ] K. Wille, DESY 81-047 ( 1981 ). [ 12 ] ARGUS CoUab., H. Albrecht et al., Nucl. Instr. Meth. A 275 (1989) 1. [ 13] Efficiency determinations and more details of the measurement can be found in K. Strahl, Dr. rer. nat. Thesis, Universittit Kadsruhe (1992), Karlsruhe preprint IEKP-KA/92-14. [14] S. Jadach and Z. W~ts, CERN-TH-5855/90 (1990). [ 15 ] S. Jadach, J.H. Kiihn and Z. Wos, CERN-TH-5856/90 (1990). [16] E. Barberio, B. van Eijk and Z. W~Is, CERN-TH5857/90 (1990). [ 17 ] M. Schmidtler (ARGUS), unpublished. [18]ARGUS Collab., H. Albrecht et al., Z. Phys. C 53 (1992) 367. [ 19 ] ARGUS CoUab., H. Albrecht et al., Phys. Lett. B 246 (1990) 278. [20] P. Privitera, Phys. Lett. B 288 (1992) 227. [211 ALEPH CoUab., D. Decamp et al., Phys. Lett. B 265 (1991) 430. [22] OPAL Collab., G. Alexander et al., Phys. Lett. B 266 (1991) 201. [23 ] DELPHI CoUab., P. Abreu et al., Z. Phys. C 55 (1992) 555. [24] L3 Collab., O. Adriani et al., Phys. Lett. B 294 (1992) 466.